The sum of the odd integers between 1 and 100 is 2500.
Here's how we can arrive at that answer:
The odd integers between 1 and 100 form an arithmetic sequence: 1, 3, 5, ..., 99.
To find the sum of an arithmetic series, we can use the formula:
S = (n/2) * (a + l)
Where:
- S is the sum of the series
- n is the number of terms in the series
- a is the first term of the series
- l is the last term of the series
In this case:
- a = 1
- l = 99
To find n, we can use the formula for the nth term of an arithmetic sequence:
an = a + (n - 1)d
Where:
- an is the nth term
- a is the first term
- n is the number of terms
- d is the common difference
In this case:
- an = 99
- a = 1
- d = 2 (since we are dealing with odd numbers)
So:
99 = 1 + (n - 1)2
98 = (n - 1)2
49 = n - 1
n = 50
Now we can plug the values into the sum formula:
S = (50/2) (1 + 99)
S = 25 100
S = 2500
Therefore, the sum of the odd integers between 1 and 100 is 2500.
